Corpus ID: 2504611

Fundamentals of Computing

  title={Fundamentals of Computing},
  author={Leonid A. Levin},
  • L. Levin
  • Published 2020
  • Computer Science
  • ArXiv
were systematically ignored. Concrete computational problems were considered only as illustrations of general principles. The notes (prepared by the students and revised by me) are skeletal: they do have (terse) proofs, but exercises, references, intuitive comments and examples are missing or inadequate. The better is English in a paragraph the smaller was my contribution and the greater caution is needed. The notes can be used by an instructor designing a course or by students who either know… Expand
1 Citations
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The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. Expand
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  • Computer Science
  • 2008 49th Annual IEEE Symposium on Foundations of Computer Science
  • 2008
The many open questions and the few things that are known about the average-case complexity of computational problems are reviewed, and a theory of completeness for distributional problems under reductions that preserveaverage-case tractability is initiated. Expand
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This paper is a personal account of some events, ideas, and academic controversies that surrounded the discovery and investigation of non-deterministic polynomial (NP)-complete problems independently by S. Cook and R. Karp in the United States and L. Levin in the Soviet Union. Expand
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An Introduction To Probability Theory And Its Applications
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This paper gives a complete description of the SMM model and its real time equivalence to the so-called successor RAMS and shows the existence of an SMM that performs integer-multiplication in linear time. Expand
N by N Checkers is Exptime Complete
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  • SIAM J. Comput.
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The question of whether a particular player can force a win from a given position and also the question of what is the best move in agiven position are considered. Expand
Theory of Recursive Functions and Effective Computability
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